Contents: Graded Rings and Modules; Flatness; Integrality: the Cohen-Seidenberg Theorems; Completions and Hensel�s Lemma; Dimension Theory I: The Main Theorem; Invertible Modules and Divisors; Noether Normalization and its Consequences; Quasi-finite Algebras and the Main Theorem of Zariski; Regular Sequences and Depth; The Cohen Macaulay Condition; Homological Theory of Regular Rings; Formal Smoothness and the Cohen Structure Theorems; Witt Rings; Derivations and Differentials

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